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qwelly [4]
1 year ago
6

WILL MARK BRAINLIEST!!!

Mathematics
2 answers:
Sergeu [11.5K]1 year ago
3 0

Answer:

The answer is the bottom graph on the left. :)

kondor19780726 [428]1 year ago
3 0

Answer:

Bottom left corner.

Step-by-step explanation:

in order to solve this, you just have to evaluate the function when x=0 that means the intersect with Y-axis, so when h(x) = x^3 + 2x^2 - 11x - 12 is evaluated for x=0

y=-12

So the point would be (0,-12)

From the graphs there are two graphs that match this description, now we just have to evaluate the intersect with X, in the bottom left it says that when y=0 x=-4

So we evaluate h(x) = x^3 + 2x^2 - 11x - 12 to x=-4 to see if it equals 0:

h(x) = x^3 + 2x^2 - 11x - 12\\h(x) = -4^3 + 2(-4)^2 - 11(-4) - 12\\h(x) = -64 +32 +44 - 12\\\\h(x)=0

As you can see the function equals 0 that means that is the graph of h(x) = x^3 + 2x^2 - 11x - 12

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Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 10x2+4xâ1, 3xâ4x2+3, and
lord [1]

I suppose

H=\mathrm{span}\{10x^2+4x-1,3x-4x^2+3,5x^2+x-1\}

The vectors that span H form a basis for P_2 if they are (1) linearly independent and (2) any vector in P_2 can be expressed as a linear combination of those vectors (i.e. they span P_2).

  • Independence:

Compute the Wronskian determinant:

\begin{vmatrix}10x^2+4x-1&3x-4x^2+3&5x^2+x-1\\20x+4&3-8x&10x+1\\20&-8&10\end{vmatrix}=-6\neq0

The determinant is non-zero, so the vectors are linearly independent. For this reason, we also know the dimension of H is 3.

  • Span:

Write an arbitrary vector in P_2 as ax^2+bx+c. Then the given vectors span P_2 if there is always a choice of scalars k_1,k_2,k_3 such that

k_1(10x^2+4x-1)+k_2(3x-4x^2+3)+k_3(5x^2+x-1)=ax^2+bx+c

which is equivalent to the system

\begin{bmatrix}10&-4&5\\4&3&1\\-1&3&-1\end{bmatrix}\begin{bmatrix}k_1\\k_2\\k_3\end{bmatrix}=\begin{bmatrix}a\\b\\c\end{bmatrix}

The coefficient matrix is non-singular, so it has an inverse. Multiplying both sides by that inverse gives

\begin{bmatrix}k_1\\k_2\\k_3\end{bmatrix}=\begin{bmatrix}-\dfrac{6a-11b+19c}3\\\dfrac{3a-5b+2c}3\\\dfrac{15a-26b+46c}3\end{bmatrix}

so the vectors do span P_2.

The vectors comprising H form a basis for it because they are linearly independent.

4 0
2 years ago
Max travels to see his brother's family by car. He drives 216 miles in 4 hours.
LUCKY_DIMON [66]

Answer:

54 mph

Step-by-step explanation:

3 0
2 years ago
What is the balance on an amortized loan of $110,000 after the first payment if the interest rate is 5.5% with a monthly P&I
marishachu [46]
The interest due on the first payment is
.. I = Prt
.. I = 110,000*.055*(1/12)
.. I = 504.17

Then the decrease in principal resulting from the first payment is
.. 568.00 -504.17 = 63.83
and the new balance is
.. $110,000.00 -63.83 = $109,936.17
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2 years ago
Malik buys and sells car parts. He bought two tires for $45.00 each and later sold them for $65.00 each. He bought three rims fo
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Solve 4/x-4=x/x-4-4/3 for x and determine if the solution is extraneous or not
4vir4ik [10]

<u>Answer:</u>

x = 4 (extraneous solution)

<u>Step-by-step explanation:</u>

\frac { 4 } { x - 4 } = \frac { x } { x - 4 } - \frac { 4 } { 3 } \\ \frac { 4 } { x - 4 } - \frac { x } { x - 4 } = - \frac { 4 } { 3 } \\ \frac { 4 - x } { x - 4 } = - \frac { 4 } { 3 } \\ 3 ( 4 - x ) = - 4 ( x - 4 ) \\ 1 2 - 3 x = - 4 x + 1 6 \\ 4 x - 3 x = 1 6 - 1 2 \\ x = 4 \\

This solution is extraneous. Reason being that even if it can be solved algebraically, it is still not a valid solution because if we substitute back x=4, we will get two fractions with zero denominator which would be undefined.

7 0
1 year ago
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